Transform-based image coding method and device for same

ABSTRACT

An image decoding method according to the present document is characterized by including: a step for receiving a bitstream including residual information; a step for deriving transform coefficients for a target block on the basis of the residual information; a step for deriving corrected transform coefficients on the basis of an inverse non-separable transform of the transform coefficients; and a step for deriving residual samples for the target block on the basis of an inverse primary transform of the corrected transform coefficients, wherein the inverse non-separable transform is performed when the size of the target block is equal to or smaller than the size of a prescribed maximum transform application block.

CROSS-REFERENCE TO RELATED APPLICATIONS

Pursuant to 35 U.S.C. § 119(e), this application is a continuation ofInternational Application PCT/KR2020/007351, with an internationalfiling date of Jun. 5, 2020, which claims the benefit of U.S.Provisional Patent Application No. 62/858,305, filed on Jun. 6, 2019,and U.S. Provisional Patent Application No. 62/870,691, filed on Jul. 4,2019, the contents of which are hereby incorporated by reference hereinin their entirety.

TECHNICAL FIELD

The present disclosure relates to an image coding technique and, moreparticularly, to a method and an apparatus for coding an image based ontransform in an image coding system.

RELATED ART

Nowadays, the demand for high-resolution and high-quality images/videossuch as 4K, 8K or more ultra high definition (UHD) images/videos hasbeen increasing in various fields. As the image/video data becomeshigher resolution and higher quality, the transmitted information amountor bit amount increases as compared to the conventional image data.Therefore, when image data is transmitted using a medium such as aconventional wired/wireless broadband line or image/video data is storedusing an existing storage medium, the transmission cost and the storagecost thereof are increased.

Further, nowadays, the interest and demand for immersive media such asvirtual reality (VR), artificial reality (AR) content or hologram, orthe like is increasing, and broadcasting for images/videos having imagefeatures different from those of real images, such as a game image isincreasing.

Accordingly, there is a need for a highly efficient image/videocompression technique for effectively compressing and transmitting orstoring, and reproducing information of high resolution and high qualityimages/videos having various features as described above.

SUMMARY

A technical aspect of the present disclosure is to provide a method andan apparatus for increasing image coding efficiency.

Another technical aspect of the present disclosure is to provide amethod and an apparatus for increasing efficiency in transform indexcoding.

Still another technical aspect of the present disclosure is to provide amethod and apparatus for coding a transform index based on a multipletransform technique.

Still another technical aspect of the present disclosure is to providean image coding method and apparatus for limiting the size of a targetblock to which non-separable transform is applied.

According to an embodiment of the present disclosure, there is providedan image decoding method performed by a decoding apparatus. The methodmay include: receiving a bitstream including residual information;deriving transform coefficients for a target block based on the residualinformation; deriving modified transform coefficients based on aninverse non-separable transform for the transform coefficients; derivingresidual samples for the target block based on an inverse primarytransform for the modified transform coefficients; and generating areconstructed picture based on the residual samples for the targetblock, wherein the inverse non-separable transform is performed when thesize of the target block is equal to or smaller than the size of apredetermined maximum transform applied block.

Here, information on the size of the maximum transform applied block isfurther received.

whether the inverse non-separable transform is performed is derived bycomparing the larger of the width or height of the target block with thewidth or height of the maximum transform applied block, and the size ofthe maximum transform applied block is 64×64.

When the size of the target block is larger than the size of thepredetermined maximum transform applied block, an lfnst index indicatinga predetermined transform kernel matrix used for the inversenon-separable transform is not derived.

The target block includes a luma coding block and a chroma coding block,when the size of the luma coding block is equal to or smaller than thesize of the maximum transform applied block and a color format is 4:2:0,the inverse non-separable transform is performed when the chroma codingblock is less than or equal to ½ of the size of the maximum transformapplied block.

According to another embodiment of the present disclosure, there isprovided an image encoding method performed by an encoding apparatus.The method may include: deriving prediction samples for a target block;deriving residual samples for the target block based on the predictionsamples; deriving transform coefficients for the target block based on aprimary transform for the residual samples; deriving modified transformcoefficients from the transform coefficients based on a predeterminedtransform kernel matrix for a non-separate transform; and encoding thequantized residual information and an lfnst index indicating thetransform kernel matrix, wherein the non-separable transform isperformed when the size of the target block is equal to or smaller thanthe size of a predetermined maximum transform applied block.

According to still another embodiment of the present disclosure, theremay be provided a digital storage medium that stores image dataincluding encoded image information and a bitstream generated accordingto an image encoding method performed by an encoding apparatus.

According to yet another embodiment of the present disclosure, there maybe provided a digital storage medium that stores image data includingencoded image information and a bitstream to cause a decoding apparatusto perform the image decoding method.

According to the present disclosure, it is possible to increase overallimage/video compression efficiency.

According to the present disclosure, it is possible to increaseefficiency in transform index coding.

A technical aspect of the present disclosure may provide a method andapparatus for coding a transform index based on a multiple transformtechnique.

A technical aspect of the present disclosure may provide an image codingmethod and apparatus for limiting the size of a target block to whichnon-separable transform is applied.

The effects that can be obtained through specific examples of thepresent disclosure are not limited to the effects listed above. Forexample, there may be various technical effects that a person havingordinary skill in the related art can understand or derive from thepresent disclosure. Accordingly, specific effects of the presentdisclosure are not limited to those explicitly described in the presentdisclosure and may include various effects that can be understood orderived from the technical features of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

FIG. 4 is schematically illustrates a multiple transform schemeaccording to an embodiment of the present document.

FIG. 5 exemplarily shows intra directional modes of 65 predictiondirections.

FIG. 6 is a diagram for explaining RST according to an embodiment of thepresent.

FIG. 7 is a flowchart illustrating an operation of a video decodingapparatus according to an embodiment of the present disclosure.

FIG. 8 is a flowchart illustrating an operation of a video encodingapparatus according to an embodiment of the present disclosure.

FIG. 9 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

While the present disclosure may be susceptible to various modificationsand include various embodiments, specific embodiments thereof have beenshown in the drawings by way of example and will now be described indetail. However, this is not intended to limit the present disclosure tothe specific embodiments disclosed herein. The terminology used hereinis for the purpose of describing specific embodiments only, and is notintended to limit technical idea of the present disclosure. The singularforms may include the plural forms unless the context clearly indicatesotherwise. The terms such as “include” and “have” are intended toindicate that features, numbers, steps, operations, elements,components, or combinations thereof used in the following descriptionexist, and thus should not be understood as that the possibility ofexistence or addition of one or more different features, numbers, steps,operations, elements, components, or combinations thereof is excluded inadvance.

Meanwhile, each component on the drawings described herein isillustrated independently for convenience of description as tocharacteristic functions different from each other, and however, it isnot meant that each component is realized by a separate hardware orsoftware. For example, any two or more of these components may becombined to form a single component, and any single component may bedivided into plural components. The embodiments in which components arecombined and/or divided will belong to the scope of the patent right ofthe present disclosure as long as they do not depart from the essence ofthe present disclosure.

Hereinafter, preferred embodiments of the present disclosure will beexplained in more detail while referring to the attached drawings. Inaddition, the same reference signs are used for the same components onthe drawings, and repeated descriptions for the same components will beomitted.

This document relates to video/image coding. For example, themethod/example disclosed in this document may relate to a VVC (VersatileVideo Coding) standard (ITU-T Rec. H.266), a next-generation video/imagecoding standard after VVC, or other video coding related standards(e.g., HEVC (High Efficiency Video Coding) standard (ITU-T Rec. H.265),EVC (essential video coding) standard, AVS2 standard, etc.).

In this document, a variety of embodiments relating to video/imagecoding may be provided, and, unless specified to the contrary, theembodiments may be combined to each other and be performed.

In this document, a video may mean a set of a series of images overtime. Generally a picture means a unit representing an image at aspecific time zone, and a slice/tile is a unit constituting a part ofthe picture. The slice/tile may include one or more coding tree units(CTUs). One picture may be constituted by one or more slices/tiles. Onepicture may be constituted by one or more tile groups. One tile groupmay include one or more tiles.

A pixel or a pel may mean a smallest unit constituting one picture (orimage). Also, ‘sample’ may be used as a term corresponding to a pixel. Asample may generally represent a pixel or a value of a pixel, and mayrepresent only a pixel/pixel value of a luma component or only apixel/pixel value of a chroma component. Alternatively, the sample mayrefer to a pixel value in the spatial domain, or when this pixel valueis converted to the frequency domain, it may refer to a transformcoefficient in the frequency domain.

A unit may represent the basic unit of image processing. The unit mayinclude at least one of a specific region and information related to theregion. One unit may include one luma block and two chroma (e.g., cb,cr) blocks. The unit and a term such as a block, an area, or the likemay be used in place of each other according to circumstances. In ageneral case, an M×N block may include a set (or an array) of samples(or sample arrays) or transform coefficients consisting of M columns andN rows.

In this document, the term “I” and “,” should be interpreted to indicate“and/or.” For instance, the expression “A/B” may mean “A and/or B.”Further, “A, B” may mean “A and/or B.” Further, “A/B/C” may mean “atleast one of A, B, and/or C.” Also, “A/B/C” may mean “at least one of A,B, and/or C.”

Further, in the document, the term “or” should be interpreted toindicate “and/or.” For instance, the expression “A or B” may include 1)only A, 2) only B, and/or 3) both A and B. In other words, the term “or”in this document should be interpreted to indicate “additionally oralternatively.”

In the present disclosure, “at least one of A and B” may mean “only A”,“only B”, or “both A and B”. In addition, in the present disclosure, theexpression “at least one of A or B” or “at least one of A and/or B” maybe interpreted as “at least one of A and B”.

In addition, in the present disclosure, “at least one of A, B, and C”may mean “only A”, “only B”, “only C”, or “any combination of A, B, andC”. In addition, “at least one of A, B, or C” or “at least one of A, B,and/or C” may mean “at least one of A, B, and C”.

In addition, a parenthesis used in the present disclosure may mean “forexample”. Specifically, when indicated as “prediction (intraprediction)”, it may mean that “intra prediction” is proposed as anexample of “prediction”. In other words, the “prediction” of the presentdisclosure is not limited to “intra prediction”, and “intra prediction”may be proposed as an example of “prediction”. In addition, whenindicated as “prediction (i.e., intra prediction)”, it may also meanthat “intra prediction” is proposed as an example of “prediction”.

Technical features individually described in one figure in the presentdisclosure may be individually implemented or may be simultaneouslyimplemented.

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

Referring to FIG. 1, the video/image coding system may include a firstdevice (source device) and a second device (receive device). The sourcedevice may deliver encoded video/image information or data in the formof a file or streaming to the receive device via a digital storagemedium or network.

The source device may include a video source, an encoding apparatus, anda transmitter. The receive device may include a receiver, a decodingapparatus, and a renderer. The encoding apparatus may be called avideo/image encoding apparatus, and the decoding apparatus may be calleda video/image decoding apparatus. The transmitter may be included in theencoding apparatus. The receiver may be included in the decodingapparatus. The renderer may include a display, and the display may beconfigured as a separate device or an external component.

The video source may obtain a video/image through a process ofcapturing, synthesizing, or generating a video/image. The video sourcemay include a video/image capture device and/or a video/image generatingdevice. The video/image capture device may include, for example, one ormore cameras, video/image archives including previously capturedvideo/images, or the like. The video/image generating device mayinclude, for example, a computer, a tablet and a smartphone, and may(electronically) generate a video/image. For example, a virtualvideo/image may be generated through a computer or the like. In thiscase, the video/image capturing process may be replaced by a process ofgenerating related data.

The encoding apparatus may encode an input video/image. The encodingapparatus may perform a series of procedures such as prediction,transform, and quantization for compression and coding efficiency. Theencoded data (encoded video/image information) may be output in the formof a bitstream.

The transmitter may transmit the encoded video/image information or dataoutput in the form of a bitstream to the receiver of the receive devicethrough a digital storage medium or a network in the form of a file orstreaming. The digital storage medium may include various storagemediums such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, and the like. Thetransmitter may include an element for generating a media file through apredetermined file format, and may include an element for transmissionthrough a broadcast/communication network. The receiver mayreceive/extract the bitstream and transmit the received/extractedbitstream to the decoding apparatus.

The decoding apparatus may decode a video/image by performing a seriesof procedures such as dequantization, inverse transform, prediction, andthe like corresponding to the operation of the encoding apparatus.

The renderer may render the decoded video/image. The renderedvideo/image may be displayed through the display.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable. Hereinafter, what is referred to as the video encodingapparatus may include an image encoding apparatus.

Referring to FIG. 2, the encoding apparatus 200 may include an imagepartitioner 210, a predictor 220, a residual processor 230, an entropyencoder 240, an adder 250, a filter 260, and a memory 270. The predictor220 may include an inter predictor 221 and an intra predictor 222. Theresidual processor 230 may include a transformer 232, a quantizer 233, adequantizer 234, an inverse transformer 235. The residual processor 230may further include a subtractor 231. The adder 250 may be called areconstructor or reconstructed block generator. The image partitioner210, the predictor 220, the residual processor 230, the entropy encoder240, the adder 250, and the filter 260, which have been described above,may be constituted by one or more hardware components (e.g., encoderchipsets or processors) according to an embodiment. Further, the memory270 may include a decoded picture buffer (DPB), and may be constitutedby a digital storage medium. The hardware component may further includethe memory 270 as an internal/external component.

The image partitioner 210 may partition an input image (or a picture ora frame) input to the encoding apparatus 200 into one or more processingunits. As one example, the processing unit may be called a coding unit(CU). In this case, starting with a coding tree unit (CTU) or thelargest coding unit (LCU), the coding unit may be recursivelypartitioned according to the Quad-tree binary-tree ternary-tree (QTBTTT)structure. For example, one coding unit may be divided into a pluralityof coding units of a deeper depth based on the quad-tree structure, thebinary-tree structure, and/or the ternary structure. In this case, forexample, the quad-tree structure may be applied first and thebinary-tree structure and/or the ternary structure may be applied later.Alternatively, the binary-tree structure may be applied first. Thecoding procedure according to the present disclosure may be performedbased on the final coding unit which is not further partitioned. In thiscase, the maximum coding unit may be used directly as a final codingunit based on coding efficiency according to the image characteristic.Alternatively, the coding unit may be recursively partitioned intocoding units of a further deeper depth as needed, so that the codingunit of an optimal size may be used as a final coding unit. Here, thecoding procedure may include procedures such as prediction, transform,and reconstruction, which will be described later. As another example,the processing unit may further include a prediction unit (PU) or atransform unit (TU). In this case, the prediction unit and the transformunit may be split or partitioned from the above-described final codingunit. The prediction unit may be a unit of sample prediction, and thetransform unit may be a unit for deriving a transform coefficient and/ora unit for deriving a residual signal from a transform coefficient.

The unit and a term such as a block, an area, or the like may be used inplace of each other according to circumstances. In a general case, anM×N block may represent a set of samples or transform coefficientsconsisting of M columns and N rows. The sample may generally represent apixel or a value of a pixel, and may represent only a pixel/pixel valueof a luma component, or only a pixel/pixel value of a chroma component.The sample may be used as a term corresponding to a pixel or a pel ofone picture (or image).

The subtractor 231 subtracts a prediction signal (predicted block,prediction sample array) output from the predictor 220 from an inputimage signal (original block, original sample array) to generate aresidual signal (residual block, residual sample array), and thegenerated residual signal is transmitted to the transformer 232. Thepredictor 220 may perform prediction on a processing target block(hereinafter, referred to as ‘current block’), and may generate apredicted block including prediction samples for the current block. Thepredictor 220 may determine whether intra prediction or inter predictionis applied on a current block or CU basis. As discussed later in thedescription of each prediction mode, the predictor may generate variousinformation relating to prediction, such as prediction mode information,and transmit the generated information to the entropy encoder 240. Theinformation on the prediction may be encoded in the entropy encoder 240and output in the form of a bitstream.

The intra predictor 222 may predict the current block by referring tosamples in the current picture. The referred samples may be located inthe neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The non-directional modes may include, for example, a DC mode and aplanar mode. The directional mode may include, for example, 33directional prediction modes or 65 directional prediction modesaccording to the degree of detail of the prediction direction. However,this is merely an example, and more or less directional prediction modesmay be used depending on a setting. The intra predictor 222 maydetermine the prediction mode applied to the current block by using theprediction mode applied to the neighboring block.

The inter predictor 221 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. The referencepicture including the reference block and the reference pictureincluding the temporal neighboring block may be same to each other ordifferent from each other. The temporal neighboring block may be calleda collocated reference block, a collocated CU (colCU), and the like, andthe reference picture including the temporal neighboring block may becalled a collocated picture (colPic). For example, the inter predictor221 may configure a motion information candidate list based onneighboring blocks and generate information indicating which candidateis used to derive a motion vector and/or a reference picture index ofthe current block. Inter prediction may be performed based on variousprediction modes. For example, in the case of a skip mode and a mergemode, the inter predictor 221 may use motion information of theneighboring block as motion information of the current block. In theskip mode, unlike the merge mode, the residual signal may not betransmitted. In the case of the motion information prediction (motionvector prediction, MVP) mode, the motion vector of the neighboring blockmay be used as a motion vector predictor and the motion vector of thecurrent block may be indicated by signaling a motion vector difference.

The predictor 220 may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Further,the predictor may be based on an intra block copy (IBC) prediction mode,or a palette mode in order to perform prediction on a block. The IBCprediction mode or palette mode may be used for content image/videocoding of a game or the like, such as screen content coding (SCC).Although the IBC basically performs prediction in a current block, itcan be performed similarly to inter prediction in that it derives areference block in a current block. That is, the IBC may use at leastone of inter prediction techniques described in the present disclosure.

The prediction signal generated through the inter predictor 221 and/orthe intra predictor 222 may be used to generate a reconstructed signalor to generate a residual signal. The transformer 232 may generatetransform coefficients by applying a transform technique to the residualsignal. For example, the transform technique may include at least one ofa discrete cosine transform (DCT), a discrete sine transform (DST), aKarhunen-Loève transform (KLT), a graph-based transform (GBT), or aconditionally non-linear transform (CNT). Here, the GBT means transformobtained from a graph when relationship information between pixels isrepresented by the graph. The CNT refers to transform obtained based ona prediction signal generated using all previously reconstructed pixels.In addition, the transform process may be applied to square pixel blockshaving the same size or may be applied to blocks having a variable sizerather than the square one.

The quantizer 233 may quantize the transform coefficients and transmitthem to the entropy encoder 240, and the entropy encoder 240 may encodethe quantized signal (information on the quantized transformcoefficients) and output the encoded signal in a bitstream. Theinformation on the quantized transform coefficients may be referred toas residual information. The quantizer 233 may rearrange block typequantized transform coefficients into a one-dimensional vector formbased on a coefficient scan order, and generate information on thequantized transform coefficients based on the quantized transformcoefficients of the one-dimensional vector form. The entropy encoder 240may perform various encoding methods such as, for example, exponentialGolomb, context-adaptive variable length coding (CAVLC),context-adaptive binary arithmetic coding (CABAC), and the like. Theentropy encoder 240 may encode information necessary for video/imagereconstruction other than quantized transform coefficients (e.g. valuesof syntax elements, etc.) together or separately. Encoded information(e.g., encoded video/image information) may be transmitted or stored ona unit basis of a network abstraction layer (NAL) in the form of abitstream. The video/image information may further include informationon various parameter sets such as an adaptation parameter set (APS), apicture parameter set (PPS), a sequence parameter set (SPS), a videoparameter set (VPS) or the like. Further, the video/image informationmay further include general constraint information. In the presentdisclosure, information and/or syntax elements which aretransmitted/signaled to the decoding apparatus from the encodingapparatus may be included in video/image information. The video/imageinformation may be encoded through the above-described encodingprocedure and included in the bitstream. The bitstream may betransmitted through a network, or stored in a digital storage medium.Here, the network may include a broadcast network, a communicationnetwork and/or the like, and the digital storage medium may includevarious storage media such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, andthe like. A transmitter (not shown) which transmits a signal output fromthe entropy encoder 240 and/or a storage (not shown) which stores it maybe configured as an internal/external element of the encoding apparatus200, or the transmitter may be included in the entropy encoder 240.

Quantized transform coefficients output from the quantizer 233 may beused to generate a prediction signal. For example, by applyingdequantization and inverse transform to quantized transform coefficientsthrough the dequantizer 234 and the inverse transformer 235, theresidual signal (residual block or residual samples) may bereconstructed. The adder 155 adds the reconstructed residual signal to aprediction signal output from the inter predictor 221 or the intrapredictor 222, so that a reconstructed signal (reconstructed picture,reconstructed block, reconstructed sample array) may be generated. Whenthere is no residual for a processing target block as in a case wherethe skip mode is applied, the predicted block may be used as areconstructed block. The adder 250 may be called a reconstructor or areconstructed block generator. The generated reconstructed signal may beused for intra prediction of a next processing target block in thecurrent block, and as described later, may be used for inter predictionof a next picture through filtering.

Meanwhile, in the picture encoding and/or reconstructing process, lumamapping with chroma scaling (LMCS) may be applied.

The filter 260 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 260 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may storethe modified reconstructed picture in the memory 270, specifically inthe DPB of the memory 270. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like. As discussed later in thedescription of each filtering method, the filter 260 may generatevarious information relating to filtering, and transmit the generatedinformation to the entropy encoder 240. The information on the filteringmay be encoded in the entropy encoder 240 and output in the form of abitstream.

The modified reconstructed picture which has been transmitted to thememory 270 may be used as a reference picture in the inter predictor221. Through this, the encoding apparatus can avoid prediction mismatchin the encoding apparatus 100 and a decoding apparatus when the interprediction is applied, and can also improve coding efficiency.

The memory 270 DPB may store the modified reconstructed picture in orderto use it as a reference picture in the inter predictor 221. The memory270 may store motion information of a block in the current picture, fromwhich motion information has been derived (or encoded) and/or motioninformation of blocks in an already reconstructed picture. The storedmotion information may be transmitted to the inter predictor 221 to beutilized as motion information of a neighboring block or motioninformation of a temporal neighboring block. The memory 270 may storereconstructed samples of reconstructed blocks in the current picture,and transmit them to the intra predictor 222.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

Referring to FIG. 3, the video decoding apparatus 300 may include anentropy decoder 310, a residual processor 320, a predictor 330, an adder340, a filter 350 and a memory 360. The predictor 330 may include aninter predictor 331 and an intra predictor 332. The residual processor320 may include a dequantizer 321 and an inverse transformer 321. Theentropy decoder 310, the residual processor 320, the predictor 330, theadder 340, and the filter 350, which have been described above, may beconstituted by one or more hardware components (e.g., decoder chipsetsor processors) according to an embodiment. Further, the memory 360 mayinclude a decoded picture buffer (DPB), and may be constituted by adigital storage medium. The hardware component may further include thememory 360 as an internal/external component.

When a bitstream including video/image information is input, thedecoding apparatus 300 may reconstruct an image correspondingly to aprocess by which video/image information has been processed in theencoding apparatus of FIG. 2. For example, the decoding apparatus 300may derive units/blocks based on information relating to block partitionobtained from the bitstream. The decoding apparatus 300 may performdecoding by using a processing unit applied in the encoding apparatus.Therefore, the processing unit of decoding may be, for example, a codingunit, which may be partitioned along the quad-tree structure, thebinary-tree structure, and/or the ternary-tree structure from a codingtree unit or a largest coding unit. One or more transform units may bederived from the coding unit. And, the reconstructed image signaldecoded and output through the decoding apparatus 300 may be reproducedthrough a reproducer.

The decoding apparatus 300 may receive a signal output from the encodingapparatus of FIG. 2 in the form of a bitstream, and the received signalmay be decoded through the entropy decoder 310. For example, the entropydecoder 310 may parse the bitstream to derive information (e.g.,video/image information) required for image reconstruction (or picturereconstruction). The video/image information may further includeinformation on various parameter sets such as an adaptation parameterset (APS), a picture parameter set (PPS), a sequence parameter set(SPS), a video parameter set (VPS) or the like. Further, the video/imageinformation may further include general constraint information. Thedecoding apparatus may decode a picture further based on information onthe parameter set and/or the general constraint information. In thepresent disclosure, signaled/received information and/or syntaxelements, which will be described later, may be decoded through thedecoding procedure and be obtained from the bitstream. For example, theentropy decoder 310 may decode information in the bitstream based on acoding method such as exponential Golomb encoding, CAVLC, CABAC, or thelike, and may output a value of a syntax element necessary for imagereconstruction and quantized values of a transform coefficient regardinga residual. More specifically, a CABAC entropy decoding method mayreceive a bin corresponding to each syntax element in a bitstream,determine a context model using decoding target syntax elementinformation and decoding information of neighboring and decoding targetblocks, or information of symbol/bin decoded in a previous step, predictbin generation probability according to the determined context model andperform arithmetic decoding of the bin to generate a symbolcorresponding to each syntax element value. Here, the CABAC entropydecoding method may update the context model using information of asymbol/bin decoded for a context model of the next symbol/bin afterdetermination of the context model. Information on prediction amonginformation decoded in the entropy decoder 310 may be provided to thepredictor (inter predictor 332 and intra predictor 331), and residualvalues, that is, quantized transform coefficients, on which entropydecoding has been performed in the entropy decoder 310, and associatedparameter information may be input to the residual processor 320. Theresidual processor 320 may derive a residual signal (residual block,residual samples, residual sample array). Further, information onfiltering among information decoded in the entropy decoder 310 may beprovided to the filter 350. Meanwhile, a receiver (not shown) whichreceives a signal output from the encoding apparatus may furtherconstitute the decoding apparatus 300 as an internal/external element,and the receiver may be a component of the entropy decoder 310.Meanwhile, the decoding apparatus according to the present disclosuremay be called a video/image/picture coding apparatus, and the decodingapparatus may be classified into an information decoder(video/image/picture information decoder) and a sample decoder(video/image/picture sample decoder). The information decoder mayinclude the entropy decoder 310, and the sample decoder may include atleast one of the dequantizer 321, the inverse transformer 322, the adder340, the filter 350, the memory 360, the inter predictor 332, and theintra predictor 331.

The dequantizer 321 may output transform coefficients by dequantizingthe quantized transform coefficients. The dequantizer 321 may rearrangethe quantized transform coefficients in the form of a two-dimensionalblock. In this case, the rearrangement may perform rearrangement basedon an order of coefficient scanning which has been performed in theencoding apparatus. The dequantizer 321 may perform dequantization onthe quantized transform coefficients using quantization parameter (e.g.,quantization step size information), and obtain transform coefficients.

The deqauntizer 322 obtains a residual signal (residual block, residualsample array) by inverse transforming transform coefficients.

The predictor may perform prediction on the current block, and generatea predicted block including prediction samples for the current block.The predictor may determine whether intra prediction or inter predictionis applied to the current block based on the information on predictionoutput from the entropy decoder 310, and specifically may determine anintra/inter prediction mode.

The predictor may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Inaddition, the predictor may perform intra block copy (IBC) forprediction on a block. The intra block copy may be used for contentimage/video coding of a game or the like, such as screen content coding(SCC). Although the IBC basically performs prediction in a currentblock, it can be performed similarly to inter prediction in that itderives a reference block in a current block. That is, the IBC may useat least one of inter prediction techniques described in the presentdisclosure.

The intra predictor 331 may predict the current block by referring tothe samples in the current picture. The referred samples may be locatedin the neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The intra predictor 331 may determine the prediction mode applied to thecurrent block by using the prediction mode applied to the neighboringblock.

The inter predictor 332 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. For example, theinter predictor 332 may configure a motion information candidate listbased on neighboring blocks, and derive a motion vector and/or areference picture index of the current block based on received candidateselection information. Inter prediction may be performed based onvarious prediction modes, and the information on prediction may includeinformation indicating a mode of inter prediction for the current block.

The adder 340 may generate a reconstructed signal (reconstructedpicture, reconstructed block, reconstructed sample array) by adding theobtained residual signal to the prediction signal (predicted block,prediction sample array) output from the predictor 330. When there is noresidual for a processing target block as in a case where the skip modeis applied, the predicted block may be used as a reconstructed block.

The adder 340 may be called a reconstructor or a reconstructed blockgenerator. The generated reconstructed signal may be used for intraprediction of a next processing target block in the current block, andas described later, may be output through filtering or be used for interprediction of a next picture.

Meanwhile, in the picture decoding process, luma mapping with chromascaling (LMCS) may be applied.

The filter 350 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 350 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may transmitthe modified reconstructed picture in the memory 360, specifically inthe DPB of the memory 360. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like.

The (modified) reconstructed picture which has been stored in the DPB ofthe memory 360 may be used as a reference picture in the inter predictor332. The memory 360 may store motion information of a block in thecurrent picture, from which motion information has been derived (ordecoded) and/or motion information of blocks in an already reconstructedpicture. The stored motion information may be transmitted to the interpredictor 260 to be utilized as motion information of a neighboringblock or motion information of a temporal neighboring block. The memory360 may store reconstructed samples of reconstructed blocks in thecurrent picture, and transmit them to the intra predictor 331.

In this specification, the examples described in the predictor 330, thedequantizer 321, the inverse transformer 322, and the filter 350 of thedecoding apparatus 300 may be similarly or correspondingly applied tothe predictor 220, the dequantizer 234, the inverse transformer 235, andthe filter 260 of the encoding apparatus 200, respectively.

As described above, prediction is performed in order to increasecompression efficiency in performing video coding. Through this, apredicted block including prediction samples for a current block, whichis a coding target block, may be generated. Here, the predicted blockincludes prediction samples in a space domain (or pixel domain). Thepredicted block may be indentically derived in the encoding apparatusand the decoding apparatus, and the encoding apparatus may increaseimage coding efficiency by signaling to the decoding apparatus notoriginal sample value of an original block itself but information onresidual (residual information) between the original block and thepredicted block. The decoding apparatus may derive a residual blockincluding residual samples based on the residual information, generate areconstructed block including reconstructed samples by adding theresidual block to the predicted block, and generate a reconstructedpicture including reconstructed blocks.

The residual information may be generated through transform andquantization procedures. For example, the encoding apparatus may derivea residual block between the original block and the predicted block,derive transform coefficients by performing a transform procedure onresidual samples (residual sample array) included in the residual block,and derive quantized transform coefficients by performing a quantizationprocedure on the transform coefficients, so that it may signalassociated residual information to the decoding apparatus (through abitstream). Here, the residual information may include valueinformation, position information, a transform technique, transformkernel, a quantization parameter or the like of the quantized transformcoefficients. The decoding apparatus may perform aquantization/dequantization procedure and derive the residual samples(or residual sample block), based on residual information. The decodingapparatus may generate a reconstructed block based on a predicted blockand the residual block. The encoding apparatus may derive a residualblock by dequantizing/inverse transforming quantized transformcoefficients for reference for inter prediction of a next picture, andmay generate a reconstructed picture based on this.

FIG. 4 schematically illustrates a multiple transform techniqueaccording to an embodiment of the present disclosure.

Referring to FIG. 4, a transformer may correspond to the transformer inthe encoding apparatus of foregoing FIG. 2, and an inverse transformermay correspond to the inverse transformer in the encoding apparatus offoregoing FIG. 2, or to the inverse transformer in the decodingapparatus of FIG. 3.

The transformer may derive (primary) transform coefficients byperforming a primary transform based on residual samples (residualsample array) in a residual block (S410). This primary transform may bereferred to as a core transform. Herein, the primary transform may bebased on multiple transform selection (MTS), and when a multipletransform is applied as the primary transform, it may be referred to asa multiple core transform.

The multiple core transform may represent a method of transformingadditionally using discrete cosine transform (DCT) type 2 and discretesine transform (DST) type 7, DCT type 8, and/or DST type 1. That is, themultiple core transform may represent a transform method of transforminga residual signal (or residual block) of a space domain into transformcoefficients (or primary transform coefficients) of a frequency domainbased on a plurality of transform kernels selected from among the DCTtype 2, the DST type 7, the DCT type 8 and the DST type 1. Herein, theprimary transform coefficients may be called temporary transformcoefficients from the viewpoint of the transformer.

In other words, when the conventional transform method is applied,transform coefficients might be generated by applying transform from aspace domain to a frequency domain for a residual signal (or residualblock) based on the DCT type 2. Unlike to this, when the multiple coretransform is applied, transform coefficients (or primary transformcoefficients) may be generated by applying transform from a space domainto a frequency domain for a residual signal (or residual block) based onthe DCT type 2, the DST type 7, the DCT type 8, and/or DST type 1.Herein, the DCT type 2, the DST type 7, the DCT type 8, and the DST type1 may be called a transform type, transform kernel or transform core.These DCT/DST transform types can be defined based on basis functions.

When the multiple core transform is performed, a vertical transformkernel and a horizontal transform kernel for a target block may beselected from among the transform kernels, a vertical transform may beperformed on the target block based on the vertical transform kernel,and a horizontal transform may be performed on the target block based onthe horizontal transform kernel. Here, the horizontal transform mayindicate a transform on horizontal components of the target block, andthe vertical transform may indicate a transform on vertical componentsof the target block. The vertical transform kernel/horizontal transformkernel may be adaptively determined based on a prediction mode and/or atransform index for the target block (CU or subblock) including aresidual block.

Further, according to an example, if the primary transform is performedby applying the MTS, a mapping relationship for transform kernels may beset by setting specific basis functions to predetermined values andcombining basis functions to be applied in the vertical transform or thehorizontal transform. For example, when the horizontal transform kernelis expressed as trTypeHor and the vertical direction transform kernel isexpressed as trTypeVer, a trTypeHor or trTypeVer value of 0 may be setto DCT2, a trTypeHor or trTypeVer value of 1 may be set to DST7, and atrTypeHor or trTypeVer value of 2 may be set to DCT8.

In this case, MTS index information may be encoded and signaled to thedecoding apparatus to indicate any one of a plurality of transformkernel sets. For example, an MTS index of 0 may indicate that bothtrTypeHor and trTypeVer values are 0, an MTS index of 1 may indicatethat both trTypeHor and trTypeVer values are 1, an MTS index of 2 mayindicate that the trTypeHor value is 2 and the trTypeVer value. Is 1, anMTS index of 3 may indicate that the trTypeHor value is 1 and thetrTypeVer value is 2, and an MTS index of 4 may indicate that bothtrTypeHor and trTypeVer values are 2.

In one example, transform kernel sets according to MTS index informationare illustrated in the following table.

TABLE 1 tu_mts_idx[ x0 ][ y0 ] 0 1 2 3 4 trTypeHor 0 1 2 1 2 trTypeVer 01 1 2 2

The transformer may derive modified (secondary) transform coefficientsby performing the secondary transform based on the (primary) transformcoefficients (S420). The primary transform is a transform from a spatialdomain to a frequency domain, and the secondary transform refers totransforming into a more compressive expression by using a correlationexisting between (primary) transform coefficients. The secondarytransform may include a non-separable transform. In this case, thesecondary transform may be called a non-separable secondary transform(NSST), or a mode-dependent non-separable secondary transform (MDNSST).The non-separable secondary transform may represent a transform whichgenerates modified transform coefficients (or secondary transformcoefficients) for a residual signal by secondary-transforming, based ona non-separable transform matrix, (primary) transform coefficientsderived through the primary transform. At this time, the verticaltransform and the horizontal transform may not be applied separately (orhorizontal and vertical transforms may not be applied independently) tothe (primary) transform coefficients, but the transforms may be appliedat once based on the non-separable transform matrix. In other words, thenon-separable secondary transform may represent a transform method inwhich the vertical and horizontal components of the (primary) transformcoefficients are not separated, and for example, two-dimensional signals(transform coefficients) are re-arranged to a one-dimensional signalthrough a certain determined direction (e.g., row-first direction orcolumn-first direction), and then modified transform coefficients (orsecondary transform coefficients) are generated based on thenon-separable transform matrix. For example, according to a row-firstorder, M×N blocks are disposed in a line in an order of a first row, asecond row, . . . , and an Nth row. According to a column-first order,M×N blocks are disposed in a line in an order of a first column, asecond column, . . . , and an Nth column. The non-separable secondarytransform may be applied to a top-left region of a block configured with(primary) transform coefficients (hereinafter, may be referred to as atransform coefficient block). For example, if the width (W) and theheight (H) of the transform coefficient block are all equal to orgreater than 8, an 8×8 non-separable secondary transform may be appliedto a top-left 8×8 region of the transform coefficient block. Further, ifthe width (W) and the height (H) of the transform coefficient block areall equal to or greater than 4, and the width (W) or the height (H) ofthe transform coefficient block is less than 8, then a 4×4 non-separablesecondary transform may be applied to a top-left min(8,W)×min(8,H)region of the transform coefficient block. However, the embodiment isnot limited to this, and for example, even if only the condition thatthe width (W) or height (H) of the transform coefficient block is equalto or greater than 4 is satisfied, the 4×4 non-separable secondarytransform may be applied to the top-left min(8,W)×min(8,H) region of thetransform coefficient block.

Specifically, for example, if a 4×4 input block is used, thenon-separable secondary transform may be performed as follows.

The 4×4 input block X may be represented as follows.

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

If the X is represented in the form of a vector, the vector

may be represented as below.

=[X ₀₀ X ₀₁ X ₀₂ X ₀₃ X ₁₀ X ₁₁ X ₁₂ X ₁₃ X ₂₀ X ₂₁ X ₂₂ X ₂₃ X ₃₀ X ₃₁X ₃₂ X ₃₃]^(T)  [Equation 2]

In Equation 2, the vector

is a one-dimensional vector obtained by rearranging the two-dimensionalblock X of Equation 1 according to the row-first order.

In this case, the secondary non-separable transform may be calculated asbelow.

=T·

  [Equation 3]

In this equation,

represents a transform coefficient vector, and T represents a 16×16(non-separable) transform matrix.

Through foregoing Equation 3, a 16×1 transform coefficient vector

may be derived, and the

may be re-organized into a 4×4 block through a scan order (horizontal,vertical, diagonal and the like). However, the above-describedcalculation is an example, and hypercube-Givens transform (HyGT) or thelike may be used for the calculation of the non-separable secondarytransform in order to reduce the computational complexity of thenon-separable secondary transform.

Meanwhile, in the non-separable secondary transform, a transform kernel(or transform core, transform type) may be selected to be modedependent. In this case, the mode may include the intra prediction modeand/or the inter prediction mode.

As described above, the non-separable secondary transform may beperformed based on an 8×8 transform or a 4×4 transform determined basedon the width (W) and the height (H) of the transform coefficient block.The 8×8 transform refers to a transform that is applicable to an 8×8region included in the transform coefficient block when both W and H areequal to or greater than 8, and the 8×8 region may be a top-left 8×8region in the transform coefficient block. Similarly, the 4×4 transformrefers to a transform that is applicable to a 4×4 region included in thetransform coefficient block when both W and H are equal to or greaterthan 4, and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block. For example, an 8×8 transform kernel matrix may be a64×64/16×64 matrix, and a 4×4 transform kernel matrix may be a16×16/8×16 matrix.

Here, to select a mode-dependent transform kernel, two non-separablesecondary transform kernels per transform set for a non-separablesecondary transform may be configured for both the 8×8 transform and the4×4 transform, and there may be four transform sets. That is, fourtransform sets may be configured for the 8×8 transform, and fourtransform sets may be configured for the 4×4 transform. In this case,each of the four transform sets for the 8×8 transform may include two8×8 transform kernels, and each of the four transform sets for the 4×4transform may include two 4×4 transform kernels.

However, as the size of the transform, that is, the size of a region towhich the transform is applied, may be, for example, a size other than8×8 or 4×4, the number of sets may be n, and the number of transformkernels in each set may be k.

The transform set may be referred to as an NSST set or an LFNST set. Aspecific set among the transform sets may be selected, for example,based on the intra prediction mode of the current block (CU orsubblock). A low-frequency non-separable transform (LFNST) may be anexample of a reduced non-separable transform, which will be describedlater, and represents a non-separable transform for a low frequencycomponent.

For reference, for example, the intra prediction mode may include twonon-directional (or non-angular) intra prediction modes and 65directional (or angular) intra prediction modes. The non-directionalintra prediction modes may include a planar intra prediction mode of No.0 and a DC intra prediction mode of No. 1, and the directional intraprediction modes may include 65 intra prediction modes of Nos. 2 to 66.However, this is an example, and this document may be applied even whenthe number of intra prediction modes is different. Meanwhile, in somecases, intra prediction mode No. 67 may be further used, and the intraprediction mode No. 67 may represent a linear model (LM) mode.

FIG. 5 exemplarily shows intra directional modes of 65 predictiondirections.

Referring to FIG. 5, on the basis of intra prediction mode 34 having aleft upward diagonal prediction direction, the intra prediction modesmay be divided into intra prediction modes having horizontaldirectionality and intra prediction modes having verticaldirectionality. In FIG. 5, H and V denote horizontal directionality andvertical directionality, respectively, and numerals −32 to 32 indicatedisplacements in 1/32 units on a sample grid position. These numeralsmay represent an offset for a mode index value. Intra prediction modes 2to 33 have the horizontal directionality, and intra prediction modes 34to 66 have the vertical directionality. Strictly speaking, intraprediction mode 34 may be considered as being neither horizontal norvertical, but may be classified as belonging to the horizontaldirectionality in determining a transform set of a secondary transform.This is because input data is transposed to be used for a verticaldirection mode symmetrical on the basis of intra prediction mode 34, andan input data alignment method for a horizontal mode is used for intraprediction mode 34. Transposing input data means that rows and columnsof two-dimensional M×N block data are switched into N×M data. Intraprediction mode 18 and intra prediction mode 50 may represent ahorizontal intra prediction mode and a vertical intra prediction mode,respectively, and intra prediction mode 2 may be referred to as a rightupward diagonal intra prediction mode because intra prediction mode 2has a left reference pixel and performs prediction in a right upwarddirection. Likewise, intra prediction mode 34 may be referred to as aright downward diagonal intra prediction mode, and intra prediction mode66 may be referred to as a left downward diagonal intra prediction mode.

According to an example, the four transform sets according to the intraprediction mode may be mapped, for example, as shown in the followingtable.

TABLE 2 lfnstPredModeIntra lfnstTrSetIdx lfnstPredModeIntra < 0 1 0 <=lfnstPredModeIntra <= 1 0  2 <= lfnstPredModeIntra <= 12 1 13 <=lfnstPredModeIntra <= 23 2 24 <= lfnstPredModeIntra <= 44 3 45 <=lfnstPredModeIntra <= 55 2 56 <= lfnstPredModeIntra <= 80 1 81 <=lfnstPredModeIntra <= 83 0

As shown in Table 2, any one of the four transform sets, that is,lfnstTrSetIdx, may be mapped to any one of four indexes, that is, 0 to3, according to the intra prediction mode.

When it is determined that a specific set is used for the non-separabletransform, one of k transform kernels in the specific set may beselected through a non-separable secondary transform index. An encodingapparatus may derive a non-separable secondary transform indexindicating a specific transform kernel based on a rate-distortion (RD)check and may signal the non-separable secondary transform index to adecoding apparatus. The decoding apparatus may select one of the ktransform kernels in the specific set based on the non-separablesecondary transform index. For example, lfnst index value 0 may refer toa first non-separable secondary transform kernel, lfnst index value 1may refer to a second non-separable secondary transform kernel, andlfnst index value 2 may refer to a third non-separable secondarytransform kernel. Alternatively, lfnst index value 0 may indicate thatthe first non-separable secondary transform is not applied to the targetblock, and lfnst index values 1 to 3 may indicate the three transformkernels.

The transformer may perform the non-separable secondary transform basedon the selected transform kernels, and may obtain modified (secondary)transform coefficients. As described above, the modified transformcoefficients may be derived as transform coefficients quantized throughthe quantizer, and may be encoded and signaled to the decoding apparatusand transferred to the dequantizer/inverse transformer in the encodingapparatus.

Meanwhile, as described above, if the secondary transform is omitted,(primary) transform coefficients, which are an output of the primary(separable) transform, may be derived as transform coefficientsquantized through the quantizer as described above, and may be encodedand signaled to the decoding apparatus and transferred to thedequantizer/inverse transformer in the encoding apparatus.

The inverse transformer may perform a series of procedures in theinverse order to that in which they have been performed in theabove-described transformer. The inverse transformer may receive(dequantized) transformer coefficients, and derive (primary) transformcoefficients by performing a secondary (inverse) transform (S450), andmay obtain a residual block (residual samples) by performing a primary(inverse) transform on the (primary) transform coefficients (S460). Inthis connection, the primary transform coefficients may be calledmodified transform coefficients from the viewpoint of the inversetransformer. As described above, the encoding apparatus and the decodingapparatus may generate the reconstructed block based on the residualblock and the predicted block, and may generate the reconstructedpicture based on the reconstructed block.

The decoding apparatus may further include a secondary inverse transformapplication determinator (or an element to determine whether to apply asecondary inverse transform) and a secondary inverse transformdeterminator (or an element to determine a secondary inverse transform).The secondary inverse transform application determinator may determinewhether to apply a secondary inverse transform. For example, thesecondary inverse transform may be an NSST, an RST, or an LFNST and thesecondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a secondarytransform flag obtained by parsing the bitstream. In another example,the secondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a transformcoefficient of a residual block.

The secondary inverse transform determinator may determine a secondaryinverse transform. In this case, the secondary inverse transformdeterminator may determine the secondary inverse transform applied tothe current block based on an LFNST (NSST or RST) transform setspecified according to an intra prediction mode. In an embodiment, asecondary transform determination method may be determined depending ona primary transform determination method. Various combinations ofprimary transforms and secondary transforms may be determined accordingto the intra prediction mode. Further, in an example, the secondaryinverse transform determinator may determine a region to which asecondary inverse transform is applied based on the size of the currentblock.

Meanwhile, as described above, if the secondary (inverse) transform isomitted, (dequantized) transform coefficients may be received, theprimary (separable) inverse transform may be performed, and the residualblock (residual samples) may be obtained. As described above, theencoding apparatus and the decoding apparatus may generate thereconstructed block based on the residual block and the predicted block,and may generate the reconstructed picture based on the reconstructedblock.

Meanwhile, in the present disclosure, a reduced secondary transform(RST) in which the size of a transform matrix (kernel) is reduced may beapplied in the concept of NSST in order to reduce the amount ofcomputation and memory required for the non-separable secondarytransform.

Meanwhile, the transform kernel, the transform matrix, and thecoefficient constituting the transform kernel matrix, that is, thekernel coefficient or the matrix coefficient, described in the presentdisclosure may be expressed in 8 bits. This may be a condition forimplementation in the decoding apparatus and the encoding apparatus, andmay reduce the amount of memory required to store the transform kernelwith a performance degradation that can be reasonably accommodatedcompared to the existing 9 bits or 10 bits. In addition, the expressingof the kernel matrix in 8 bits may allow a small multiplier to be used,and may be more suitable for single instruction multiple data (SIMD)instructions used for optimal software implementation.

In the present specification, the term “RST” may mean a transform whichis performed on residual samples for a target block based on a transformmatrix whose size is reduced according to a reduced factor. In the caseof performing the reduced transform, the amount of computation requiredfor transform may be reduced due to a reduction in the size of thetransform matrix. That is, the RST may be used to address thecomputational complexity issue occurring at the non-separable transformor the transform of a block of a great size.

RST may be referred to as various terms, such as reduced transform,reduced secondary transform, reduction transform, simplified transform,simple transform, and the like, and the name which RST may be referredto as is not limited to the listed examples. Alternatively, since theRST is mainly performed in a low frequency region including a non-zerocoefficient in a transform block, it may be referred to as aLow-Frequency Non-Separable Transform (LFNST). The transform index maybe referred to as an LFNST index.

Meanwhile, when the secondary inverse transform is performed based onRST, the inverse transformer 235 of the encoding apparatus 200 and theinverse transformer 322 of the decoding apparatus 300 may include aninverse reduced secondary transformer which derives modified transformcoefficients based on the inverse RST of the transform coefficients, andan inverse primary transformer which derives residual samples for thetarget block based on the inverse primary transform of the modifiedtransform coefficients. The inverse primary transform refers to theinverse transform of the primary transform applied to the residual. Inthe present disclosure, deriving a transform coefficient based on atransform may refer to deriving a transform coefficient by applying thetransform.

FIG. 6 is a diagram illustrating an RST according to an embodiment ofthe present disclosure.

In the present disclosure, a “target block” may refer to a current blockto be coded, a residual block, or a transform block.

In the RST according to an example, an N-dimensional vector may bemapped to an R-dimensional vector located in another space, so that thereduced transform matrix may be determined, where R is less than N. Nmay mean the square of the length of a side of a block to which thetransform is applied, or the total number of transform coefficientscorresponding to a block to which the transform is applied, and thereduced factor may mean an R/N value. The reduced factor may be referredto as a reduced factor, reduction factor, simplified factor, simplefactor or other various terms. Meanwhile, R may be referred to as areduced coefficient, but according to circumstances, the reduced factormay mean R. Further, according to circumstances, the reduced factor maymean the N/R value.

In an example, the reduced factor or the reduced coefficient may besignaled through a bitstream, but the example is not limited to this.For example, a predefined value for the reduced factor or the reducedcoefficient may be stored in each of the encoding apparatus 200 and thedecoding apparatus 300, and in this case, the reduced factor or thereduced coefficient may not be signaled separately.

The size of the reduced transform matrix according to an example may beR×N less than N×N, the size of a conventional transform matrix, and maybe defined as in Equation 4 below.

$\begin{matrix}{T_{R \times N} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \ldots & t_{1N} \\t_{21} & t_{22} & t_{23} & \; & t_{2N} \\\; & \vdots & \; & \ddots & \vdots \\t_{R\; 1} & t_{R\; 2} & t_{R\; 3} & \ldots & t_{RN}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

The matrix T in the Reduced Transform block shown in FIG. 6(a) may meanthe matrix T_(R×N) of Equation 4. As shown in FIG. 6(a), when thereduced transform matrix T_(R×N) is multiplied to residual samples forthe target block, transform coefficients for the target block may bederived.

In an example, if the size of the block to which the transform isapplied is 8×8 and R=16 (i.e., R/N=16/64=¼), then the RST according toFIG. 6(a) may be expressed as a matrix operation as shown in Equation 5below. In this case, memory and multiplication calculation can bereduced to approximately ¼ by the reduced factor.

In the present disclosure, a matrix operation may be understood as anoperation of multiplying a column vector by a matrix, disposed on theleft of the column vector, to obtain a column vector.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{1,2} & t_{1,3} & \ldots & t_{1,64} \\t_{2,1} & t_{2,2} & t_{2,3} & \; & t_{2,64} \\\; & \vdots & \; & \ddots & \vdots \\t_{16,1} & t_{16,2} & t_{16,3} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}r_{1} \\r_{2} \\\vdots \\r_{64}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

In Equation 5, r₁ to r₆₄ may represent residual samples for the targetblock and may be specifically transform coefficients generated byapplying a primary transform. As a result of the calculation of Equation5 transform coefficients ci for the target block may be derived, and aprocess of deriving ci may be as in Equation 6.

EQUATION 6   for i from to R  c_(i)=0  for j from 1 to N   c_(i) +=t_(i,j) * r_(j)

As a result of the calculation of Equation 6, transform coefficients c₁to c_(R) for the target block may be derived. That is, when R=16,transform coefficients c₁ to c₁₆ for the target block may be derived.If, instead of RST, a regular transform is applied and a transformmatrix of 64×64 (N×N) size is multiplied to residual samples of 64×1(N×1) size, then only 16 (R) transform coefficients are derived for thetarget block because RST was applied, although 64 (N) transformcoefficients are derived for the target block. Since the total number oftransform coefficients for the target block is reduced from N to R, theamount of data transmitted by the encoding apparatus 200 to the decodingapparatus 300 decreases, so efficiency of transmission between theencoding apparatus 200 and the decoding apparatus 300 can be improved.

When considered from the viewpoint of the size of the transform matrix,the size of the regular transform matrix is 64×64 (N×N), but the size ofthe reduced transform matrix is reduced to 16×64 (R×N), so memory usagein a case of performing the RST can be reduced by an R/N ratio whencompared with a case of performing the regular transform. In addition,when compared to the number of multiplication calculations N×N in a caseof using the regular transform matrix, the use of the reduced transformmatrix can reduce the number of multiplication calculations by the R/Nratio (R×N).

In an example, the transformer 232 of the encoding apparatus 200 mayderive transform coefficients for the target block by performing theprimary transform and the RST-based secondary transform on residualsamples for the target block. These transform coefficients may betransferred to the inverse transformer of the decoding apparatus 300,and the inverse transformer 322 of the decoding apparatus 300 may derivethe modified transform coefficients based on the inverse reducedsecondary transform (RST) for the transform coefficients, and may deriveresidual samples for the target block based on the inverse primarytransform for the modified transform coefficients.

The size of the inverse RST matrix T_(N×R) according to an example isN×R less than the size N×N of the regular inverse transform matrix, andis in a transpose relationship with the reduced transform matrix T_(R×N)shown in Equation 4.

The matrix T^(t) in the Reduced Inv. Transform block shown in FIG. 6(b)may mean the inverse RST matrix T_(R×N) ^(T) (the superscript T meanstranspose). When the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block as shown in FIG. 6(b),the modified transform coefficients for the target block or the residualsamples for the current block may be derived. The inverse RST matrixT_(R×N) ^(T) may be expressed as (T_(R×N) ^(T))_(N×R).

More specifically, when the inverse RST is applied as the secondaryinverse transform, the modified transform coefficients for the targetblock may be derived when the inverse RST matrix T_(R×N) ^(T) ismultiplied to the transform coefficients for the target block.Meanwhile, the inverse RST may be applied as the inverse primarytransform, and in this case, the residual samples for the target blockmay be derived when the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block.

In an example, if the size of the block to which the inverse transformis applied is 8×8 and R=16 (i.e., R/N=16/64=¼), then the RST accordingto FIG. 6(b) may be expressed as a matrix operation as shown in Equation7 below.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{2,1} & \; & t_{16,1} \\t_{1,2} & t_{2,2} & \ldots & t_{16,2} \\t_{1,3} & t_{2,3} & \; & t_{16,3} \\\vdots & \vdots & \; & \vdots \\\; & \vdots & \ddots & \vdots \\t_{1,64} & t_{2,64} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}c_{1} \\c_{2} \\\vdots \\c_{16}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

In Equation 7, c₁ to C₁₆ may represent the transform coefficients forthe target block. As a result of the calculation of Equation 7, r_(i)representing the modified transform coefficients for the target block orthe residual samples for the target block may be derived, and theprocess of deriving r_(i) may be as in Equation 8.

EQUATION 8   For i from 1 to N  r_(i)=0  for j from 1 to R   r_(i) +=t_(j,i) * c_(j)

As a result of the calculation of Equation 8, r_(i) to r_(N)representing the modified transform coefficients for the target block orthe residual samples for the target block may be derived. Whenconsidered from the viewpoint of the size of the inverse transformmatrix, the size of the regular inverse transform matrix is 64×64 (N×N),but the size of the reduced inverse transform matrix is reduced to 64×16(R×N), so memory usage in a case of performing the inverse RST can bereduced by an R/N ratio when compared with a case of performing theregular inverse transform. In addition, when compared to the number ofmultiplication calculations N×N in a case of using the regular inversetransform matrix, the use of the reduced inverse transform matrix canreduce the number of multiplication calculations by the R/N ratio (N×R).

A transform set configuration shown in Table 2 may also be applied to an8×8 RST. That is, the 8×8 RST may be applied according to a transformset in Table 2. Since one transform set includes two or three transforms(kernels) according to an intra prediction mode, it may be configured toselect one of up to four transforms including that in a case where nosecondary transform is applied. In a transform where no secondarytransform is applied, it may be considered to apply an identity matrix.Assuming that indexes 0, 1, 2, and 3 are respectively assigned to thefour transforms (e.g., index 0 may be allocated to a case where anidentity matrix is applied, that is, a case where no secondary transformis applied), a transform index or an lfnst index as a syntax element maybe signaled for each transform coefficient block, thereby designating atransform to be applied. That is, for a top-left 8×8 block, through thetransform index, it is possible to designate an 8×8 RST in an RSTconfiguration, or to designate an 8×8 lfnst when the LFNST is applied.The 8×8 lfnst and the 8×8 RST refer to transforms applicable to an 8×8region included in the transform coefficient block when both W and H ofthe target block to be transformed are equal to or greater than 8, andthe 8×8 region may be a top-left 8×8 region in the transform coefficientblock. Similarly, a 4×4 lfnst and a 4×4 RST refer to transformsapplicable to a 4×4 region included in the transform coefficient blockwhen both W and H of the target block to are equal to or greater than 4,and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block.

According to an embodiment of the present disclosure, for a transform inan encoding process, only 48 pieces of data may be selected and amaximum 16×48 transform kernel matrix may be applied thereto, ratherthan applying a 16×64 transform kernel matrix to 64 pieces of dataforming an 8×8 region. Here, “maximum” means that m has a maximum valueof 16 in an m×48 transform kernel matrix for generating m coefficients.That is, when an RST is performed by applying an m×48 transform kernelmatrix (m<16) to an 8×8 region, 48 pieces of data are input and mcoefficients are generated. When m is 16, 48 pieces of data are inputand 16 coefficients are generated. That is, assuming that 48 pieces ofdata form a 48×1 vector, a 16×48 matrix and a 48×1 vector aresequentially multiplied, thereby generating a 16×1 vector. Here, the 48pieces of data forming the 8×8 region may be properly arranged, therebyforming the 48×1 vector. For example, a 48×1 vector may be constructedbased on 48 pieces of data constituting a region excluding the bottomright 4×4 region among the 8×8 regions. Here, when a matrix operation isperformed by applying a maximum 16×48 transform kernel matrix, 16modified transform coefficients are generated, and the 16 modifiedtransform coefficients may be arranged in a top-left 4×4 regionaccording to a scanning order, and a top-right 4×4 region and abottom-left 4×4 region may be filled with zeros.

For an inverse transform in a decoding process, the transposed matrix ofthe foregoing transform kernel matrix may be used. That is, when aninverse RST or LFNST is performed in an inverse transform processperformed by the decoding apparatus, input coefficient data to which theinverse RST is applied is configured in a one-dimensional vectoraccording to a predetermined arrangement order, and a modifiedcoefficient vector obtained by multiplying the one-dimensional vectorand a corresponding inverse RST matrix on the left of theone-dimensional vector may be arranged in a two-dimensional blockaccording to a predetermined arrangement order.

In summary, in the transform process, when an RST or LFNST is applied toan 8×8 region, a matrix operation of 48 transform coefficients intop-left, top-right, and bottom-left regions of the 8×8 region excludingthe bottom-right region among transform coefficients in the 8×8 regionand a 16×48 transform kernel matrix. For the matrix operation, the 48transform coefficients are input in a one-dimensional array. When thematrix operation is performed, 16 modified transform coefficients arederived, and the modified transform coefficients may be arranged in thetop-left region of the 8×8 region.

On the contrary, in the inverse transform process, when an inverse RSTor LFNST is applied to an 8×8 region, 16 transform coefficientscorresponding to a top-left region of the 8×8 region among transformcoefficients in the 8×8 region may be input in a one-dimensional arrayaccording to a scanning order and may be subjected to a matrix operationwith a 48×16 transform kernel matrix. That is, the matrix operation maybe expressed as (48×16 matrix)*(16×1 transform coefficient vector)=(48×1modified transform coefficient vector). Here, an n×1 vector may beinterpreted to have the same meaning as an n×1 matrix and may thus beexpressed as an n×1 column vector. Further, * denotes matrixmultiplication. When the matrix operation is performed, 48 modifiedtransform coefficients may be derived, and the 48 modified transformcoefficients may be arranged in top-left, top-right, and bottom-leftregions of the 8×8 region excluding a bottom-right region.

When a secondary inverse transform is based on an RST, the inversetransformer 235 of the encoding apparatus 200 and the inversetransformer 322 of the decoding apparatus 300 may include an inversereduced secondary transformer to derive modified transform coefficientsbased on an inverse RST on transform coefficients and an inverse primarytransformer to derive residual samples for the target block based on aninverse primary transform on the modified transform coefficients. Theinverse primary transform refers to the inverse transform of a primarytransform applied to a residual. In the present disclosure, deriving atransform coefficient based on a transform may refer to deriving thetransform coefficient by applying the transform.

On the other hand, when applying the LFNST, it is possible to limit themaximum size of the target block to which the non-separable secondarytransform is applied.

For example, when the height and width of a target block, eg, a codingunit, a coding block, a transform unit, or a transform block, is equalto or less than 64, a method of applying the LFNST only may be proposed.

Alternatively, according to another example, a method of applying theLFNST only when the size of the target block is smaller than 128×128 maybe proposed. That is, at least one of the width and the height is lessthan 128, and a method of applying the LFNST only to the case where boththe width and the height are equal to or less than 128 may be proposed.

Alternatively, according to an example, the maximum applied block sizeto which the LFNST is applied may be limited to information such asmax_width and max_height rather than a specific value. That is, it canbe configured to apply LFNST only when width <=max_width and height<=max_height. In this case, information on max_width and/or informationon max_height may be signaled from the encoding apparatus to thedecoding apparatus.

As such, the specification text in case where the size of the targetblock to which LFNST is applied is as follows.

TABLE 3 Coding unit syntax Descriptor coding_unit( x0, y0, cbWidth,cbHeight, treeType ) { ...     }    }       numSigCoeff = 0      numZeroOutSigCoeff = 0    transform_tree( x0, y0, cbWidth,cbHeight, treeType )       lfnstWidth = ( treeType == DUAL_TREE_CHROMA )?         cbWidth/SubWidth : cbWidth       lfnstHeight = ( treeType ==DUAL_TREE_CHROMA ) ?           cbHeight/SubHeight : cbHeight       ifMin( lfnstWidth, lfnstHeight) >= 4       && sps_lfnst_enabled_flag == 1&&     CuPredMode[ x0 ][ y0 ] == MODE_INTRA &&    IntraSubPartitionsSplitType == ISP_NO_SPLIT &&     !intra_mip_flag[x0 ][ y0 ] && Max( cbWidth, cbHeight ) <= 64 ) {         if( (numSigCoeff >( ( treeType ==         SINGLE_TREE ) ? 2 : 1 ) ) &&     numZeroOutSigCoeff == 0 ) {          lfnst_Idx[ x0 ][ y0 ] ae (v)        }      }   }  } }

As shown in Table 3, lfnst_idx[x0][y0] may be signaled in the codingunit syntax. lfnst_idx[x0][y0] may indicate any one of two transformkernel matrices included in the transform set, and when lfnst_idx is 0,it may indicate that non-separable secondary transform, that is, theLFNST is not applied. When lfnst_idx[x0][y0] does not exist, it isinferred to be a value of 0.

In addition, the maximum coding block size in which lfnst_idx[x0][y0]can be coded is limited to 64×64 (Max(cbWidth, cbHeight)<=64). That is,by adding Max(cbWidth, cbHeight)<=64 to the if clause condition forlfnst_idx to be coded, the size of the maximum applied block is limitedto 64×64.

In this embodiment, since the width (cbWidth) of the coding block andthe height (cbHeight) of the coding block indicate the width of thecoding block and the height of the coding block for the luma component,respectively, in the case of the chroma component, LFNST may be appliedto each block having a smaller size according to the image color format(eg, 4:2:0).

Specifically, as shown in Table 3, if the tree type of the target blockis dual tree chroma, the LFNST can be applied to the chroma block of thesize divided by SubWidthC and SubHeight, which indicates the variablefor the chroma format in the size of the luma coding block[lfnstWidth=(treeType==DUAL_TREE_CHROMA) ? cbWidth/SubWidthC: cbWidth,lfnstHeight=(treeType==DUAL_TREE_CHROMA) ? cbHeight/SubHeightC:cbHeight].

If the color format is 4:2:0, since SubWidthC and SubHeight are 2, theLFNST may be applied to a chroma block having a width and heightobtained by dividing the width and height of the luma block by 2.Accordingly, since the LFNST may be applied when the size of the lumablock is equal to or smaller than the 64×64 block, the LFNST may beapplied when the size of the chroma block is equal to or smaller thanthe 32×32 block when the color format is 4:2:0.

Meanwhile, in this document, when the horizontal and vertical lengths ofblock A are Wa and Ha, respectively, and the horizontal and verticallengths of block B are Wb and Hb, respectively, block A is smaller thanblock B means that Wa is equal to or smaller than Wb and Ha is equal toor smaller than Hb, and Wa and Wb are not equal or Ha and Hb are notequal. In addition, the meaning that block A is smaller than or equal toblock B indicates that Wa is equal to or smaller than Wb and Ha is equalto or smaller than Hb.

In summary, when the size of the target block is equal to or smallerthan the preset maximum size, the LFNST may be applied, this maximumsize may be applied to the size of the luma block, and correspondingly,the maximum size of the chroma block to which the LFNST may be appliedmay be derived.

On the other hand, unlike Table 3, the maximum block size condition towhich the LFNST is applied to the luma component and the chromacomponent may be separately provided through separate syntaxinformation. That is, for the luma component and the chroma component,the maximum size information to which the LFNST can be applied may besignaled separately.

According to another example, If the LFNST is not applied only to acoding block in which both the width and height of the target block are128, that is, if it is configured to apply the LFNST only to blockssmaller than 128×128, the if clause is can be configured as.

TABLE 4 if( Min( lfnstWidth, lfnsttHeight ) >= && 4sps_lfnst_enabled_flag == 1 &&  CuPredMode[ x0 ][ y0 ] == MODE_INTRA &&  IntraSubPartitionsSplitType == ISP_NO_SPLIT &&   !intra_mip_flag[ x0][ y0 ] && Max( cbWidth, cbHeight ) <= 128 &&   ( cbWidth < 128 cbHeight< 128 ) ) {   if( ( numSigCoeff > ( ( treeType == SINGLE_TREE ) ? 2: 1 )) &&     numZeroOutSigCoeff == 0 ) {    lfnst_Idx[ x0 ][ y0 ] ae (v) }

This lfnst_idx may be signaled at the transform unit level according toanother example.

TABLE 5 Transform unit syntax Descriptor transform_unit( x0, y0,cbWidth, cbHeight, treeType, subTuIndex )  if( ( treeType == STNGLE_TREE| | treeType == DUAL_TREE_CHROMA ) {   if( ( IntraSubPartitionsSplitType= = ISP_NO_SPLIT && |( cu_sbt_flag &&       ( ( subTuIndex == 0 &&cu_sbt_pos_flag ) | |        ( subTuIndex == 1 && |cu_sbt_pos_flag ) ) )) | |     ( IntraSubPartitionsSplitType |= ISP_NO_SPLIT &&      (subTuIndex == NumIntraSubPartitions − 1 ) ) ) {     tu_cbf_cb[ x0 ][ y0] ae (v)     tu_cbf_cr[ x0 ][ y0 ] ae (v)   }  ...  }  numSigCoeff = 0 numZeroOutSigCoeff = 0  if( tu_cbf_luma[ x0 ][ y0 ] ) {   if(!transform_skip_flag[ x0 ][ y0 ] )     residual_coding( x0, y0, Log2(tbWidth ), Log2( tbHeight ), 0 )   else     residual_ts_coding( x0, y0,Log2( tbWidth ), Log2( tbHeight ), 0 )  }  if( tu_cbf_cb[ x0 ][ y0 ] )  residual_coding( xC, yC, Log2( wC ), Log2( hC ), 1 )  if( tu_cbf_cb[x0 ][ y0 ] ) {   if( tu_cbf_cb[ x0 ][ y0 ] )     tu_joint_cbcr_residual[x0 ][ y0 ]   if( !tu_joint_cbcr_residual[ x0 ][ y0 ] )    residual_coding( xC, yC, Log2( wC ), Log2( hC ), 2 )  }  lfnstWidth= ( treeType == DUAL_TREE_CHROMA ) ? wC : tbWidth  lfnstHeight = (treeType == DUAL_TREE_CHROMA ) ? hC : tbHeight  if( Min( lfnstWidth,lfnstHeight ) >= 4 && sps_lfnst_enabled_flag == 1 &&   CuPredMode[ x0 ][y0 ] == MODE_INTRA &&   IntraSubPartitionsSplitType == ISP_NO_SPLIT &&  !intra_mip_flag[ x0 ][ y0 ] ) {    if( ( numSigCoeff > ( ( treeType ==SINGLE_TREE ) ? 2: 1 ) ) &&      numZeroOutSigCoeff == 0 ) {     lfnst_Idx[ x0 ][ y0 ] ae (v)    }  } }

As shown in Table 5, the coding part for lfnst_idx[x0] [y0] may be movedfrom the coding unit syntax to the transform unit syntax. That is,lfnst_idx[x0] [y0] may be signaled at the transform unit level.

The width (lfnstWidth) and height (lfnstHeight) of the target block towhich the LFNST is applied may vary depending on the tree type. In thecase of a dual tree chroma block, the width (lfnstWidth) and height(lfnstHeight) of the target block are set to the width (wC) of thechroma transformation block and the height (hC) of the chromatransformation block, and in other cases, the width (lfnstWidth) andheight (lfnstHeight) of the target block can be limited by the width(tbWidth) or height (tbHeight) of the transformation block[lfnstWidth=(treeType==DUAL_TREE_CHROMA) ? wC: tbWidth,lfnstHeight=(treeType DUAL_TREE_CHROMA) ? hC: tbHeight]. In this case,the width wC of the chroma transform block and the height hC of thechroma transform block are corrected based on SubWidthC and SubHeightCto reflect the color format.

When the coding and signaling of the LFNST index moves to the transformunit level, in case that a large-size coding unit is divided intoseveral transform units, for example, when a coding unit of a size of128×128 is divided into four 64×64 transformation units since the sizeof the maximum transformable block is 64, that is, when transform unittiling occurs, the LFNST can be applied to the corresponding transformunits, and since the LFNST index is signaled for each transform unit, adifferent transform kernel can be applied to each transform unit.

Alternatively, according to an example, as described above, the LFNSTindex may be signaled at the coding unit level, and the width and heightof the target block to which the LFNST is applied may be limited to thesize of the transform block, for example, the maximum size of thetransform block.

The maximum size of the transform block may be explicitly signaled fromthe encoding apparatus to the decoding apparatus or may be implicitlyderived. For example, index information or flag information may besignaled for signaling the maximum size of the transform block, and whenthe maximum size of the transform block is derived based on thisinformation, the LFNST may be performed based thereon.

The table below shows this as an example.

TABLE 6 Coding unit syntax if( Min( lfnstWidth, lfnstHeight ) >= 4 &&sps_lfnst_enabled_flag == 1 &&   CuPredMode[ chType ][ x0 ][ y0 ] ==MODE_INTRA   && lfnstNotTaFlag == 1 &&   ( treeType == DUAL_TREE_CHROMA| | !intra_mip_flag[ x0 ][ y0 ] | |    Min( lfnstWidth, lfnstHeight ) >=16 ) &&   Max( cbWidth, cbHeight ) <= MaxTbSizeY) {  if( (IntraSubPartitionsSplitType != ISP_NO_SPLIT | | LfnstDoOnly == 0 ) &&   LfnstZeroOutCoeffFlag == 1 )   lfnst_Idx ae (v) }

As shown in Table 6, lfnst_idx is signaled only when the maximum valuesof the width and height of the coding unit are equal to or smaller thanthe maximum size of the transform block, and the LFNST can be performedon the target block [Max(cbWidth, cbHeight) MaxTbSizeY].

The maximum size (MaxTbSizeY) of such a transform block may be derivedfrom flag information at a higher level such as a sequence parameterset, for example, syntax information such assps_max_luma_transform_size_64_flag. According to an example, themaximum size of the transform block may be 64×64 or 32×32.

The following drawings are provided to describe specific examples of thepresent disclosure. Since the specific designations of devices or thedesignations of specific signals/messages/fields illustrated in thedrawings are provided for illustration, technical features of thepresent disclosure are not limited to specific designations used in thefollowing drawings.

FIG. 7 is a flowchart illustrating an operation of a video decodingapparatus according to an embodiment of the present disclosure.

Each operation illustrated in FIG. 7 may be performed by the decodingapparatus 300 illustrated in FIG. 3. Specifically, S710 may be performedby the entropy decoder 310 illustrated in FIG. 3, S720 may be performedby the dequantizer 321 illustrated in FIGS. 3, S730 and S740 may beperformed by the inverse transformer 322 illustrated in FIGS. 3 and S750may be performed by the adder 340 illustrated in FIG. 3. Operationsaccording to S710 to S750 are based on some of the foregoing detailsexplained with reference to FIG. 4 to FIG. 6. Therefore, a descriptionof specific details overlapping with those explained above withreference to FIG. 3 to FIG. 6 will be omitted or will be made briefly.

The decoding apparatus 300 according to an embodiment may receive abitstream including residual information and derive quantized transformcoefficients for a target block from the bitstream (S710).

More specifically, the decoding apparatus 300 may decode information onquantized transform coefficients for the target block from the bitstreamand may derive the quantized transform coefficients for the target blockbased on the information on the quantized transform coefficients for thetarget block. The information on the quantized transform coefficientsfor the target block may be included in a sequence parameter set (SPS)or a slice header and may include at least one of information on whethera reduced transform (RST) is applied, information on the simplificationfactor, information on a minimum transform size in which the reducedtransform is applied, information on a maximum transform size in whichthe reduced transform is applied, a reduced inverse transform size, andinformation on a transform index indicating any one of transform kernelmatrices included in a transform set.

The decoding apparatus 300 further receives information about the LFNSTindex and the intra prediction mode from the bitstream. Further, thedecoding apparatus 300 may further receive MTS index informationindicating a transform kernel of an inverse primary transform.

The LFNST index information is received as syntax information and thesyntax information is received as a binarized bin string including 0 and1.

The syntax element of the LFNST index according to this embodiment mayindicate whether an inverse LFNST or an inverse non-separable transformis applied and any one of a transform kernel matrix included in thetransform set, and the transform set includes two transform kernelmatrices. In this case, the syntax element of the transform index mayhave three values.

That is, according to an embodiment, the syntax element value for theLFNST index may be include 0 indicating a case in which the inverseLFNST is not applied to the target block, 1 indicating the firsttransformation kernel matrix among the transformation kernel matrices,and 2 indicating the second transform kernel matrix among thetransformation kernel matrices.

The decoding apparatus 300 according to an embodiment may derivetransform coefficients by performing dequantization on the quantizedtransform coefficients of the target block (S720).

The decoding apparatus 300 according to an embodiment, when a size of atarget block is equal to or smaller than a size of a predeterminedmaximum transform applied block, can be derived modified transformcoefficients based on the inverse non-separable transform or inverseLFNST on transform coefficients (S730).

The decoding apparatus 300 may further receive information on the sizeof the maximum transform applied block, and this information may besignaled at the sequence parameter set level with a syntax such assps_max_luma_transform_size_64_flag.

Also, the size of the maximum transform applied block may be set to thesize of the transform block, for example, the maximum size of thetransform block. For example, if the size of the maximum transform blockis 64×64, the size of the maximum transform applied block is set to64×64 or 64, and if the size of the maximum transform block is 32×32,the size of the maximum transform applied block may be set to 32×32 or32.

The decoding apparatus 300 may determine whether the inversenon-separable transform is performed through comparison of any one ofthe width or height of the target block, for example, a large value withthe size of the maximum transform applied block, that is, the width orheight of the maximum transform applied block.

Alternatively, if the size of the target block is larger than the sizeof the predetermined maximum transform applied block, the lfnst indexindicating the predetermined transform kernel matrix used for theinverse non-separable transform may not be derived. That is, if the sizeof the target block is larger than the size of the predetermined maximumtransform applied block, the lfnst index may not be signaled. If thelfnst index is not derived, the lfnst index is inferred to as 0 and theLFNST is not applied to the target block.

Meanwhile, the target block may be a coding block according to anexample, and may be a luma coding block and a chroma coding blockaccording to a color index. According to an example, if the size of theluma coding block is less than or equal to the size of the maximumtransform applied block and the color format is 4:2:0, the inversenon-separable transform may be performed on the chroma coding block whenit is less than or equal to ½ the size of the maximum transform appliedblock. That is, the inverse LFNST may be applied to the chroma blockhaving a width and a height obtained by dividing the width and height ofthe luma block by two. For example, since the inverse LFNST can beapplied when the size of the luma block is equal to or smaller than the64×64 block, the inverse LFNST can be applied when the size of thechroma block is equal to or smaller than the 32×32 block when the colorformat is 4:2:0.

The inverse transformer 332 of the decoding apparatus 300 may determinea transform set based on a mapping relationship according to an intraprediction mode applied to a target block, and may perform an inverseLFNST, that is, the inverse non-separable transformation based on thetransform set and the values of syntax elements for the LFNST index.

As described above, a plurality of transform sets may be determinedaccording to an intra prediction mode of a transform block to betransformed, and an inverse LFNST may be performed based on any one oftransform kernel matrices included in a transform set indicated by anLFNST index.

In one example, the inverse non-separable transform or the inverse LFNSTmay be performed based on an inverse LFNST matrix and the inverse LFNSTmatrix may be a non-square matrix in which the number of columns is lessthan the number of rows.

In one embodiment, S730 may include decoding the transform index,determining whether it corresponds to the conditions to apply theinverse RST based on the transform index, that is, the LFNST index,selecting a transform kernel matrix and applying the inverse LFNST tothe transform coefficients based on the selected transform kernel matrixand/or the simplification factor when the conditions for applying theinverse LFNST is satisfied. In this case, the size of the simplificationinverse transform matrix may be determined based on the simplificationfactor.

On the other hand, when the LFNST is not applied, only the MTS-basedprimary inverse transform procedure may be applied in the inversetransform procedure as follows. That is, the decoding apparatus maydetermine whether the LFNST is applied to the current block as in theabove-described embodiment, and when the LFNST is not applied, thedecoding apparatus may derive residual samples from transformcoefficients through a primary inverse transform.

The primary inverse transform procedure may be referred to as an inverseprimary transform procedure or an inverse MTS transform procedure. Suchan MTS-based primary inverse transform procedure may also be omitted insome cases.

The decoding apparatus 300 according to an embodiment may deriveresidual samples for the target block based on the inverse primarytransform of the modified transform coefficients (S740).

The decoding apparatus 300 may perform an inverse primary transform onthe modified transform coefficients for the target block. In this case,a simplified inverse transform may be applied to the inverse primarytransform, or a conventional separable transform may be used.

The decoding apparatus 300 according to an embodiment may generatereconstructed samples based on residual samples of the target block andprediction samples of the target block (S750).

Referring to S730, it can be confirmed that residual samples for thetarget block are derived based on the inverse LFNST of the transformcoefficients for the target block. Regarding the size of an inversetransform matrix, the size of a general inverse transform matrix is N×N,while the size of an inverse LFNST matrix is reduced to N×R, thus makingit possible to reduce memory occupancy by an R/N ratio when performingthe inverse LFNST compared to when performing a general transform.Further, compared to the number of multiplication operations, N×N, whenusing the general inverse transform matrix, it is possible to reduce thenumber of multiplication operations by an R/N ratio (to N×R) when theinverse LFNST matrix is used. In addition, since only R transformcoefficients need to be decoded when the inverse LFNST is applied, thetotal number of transform coefficients for the target block may bereduced from N to R, compared to when the general inverse transform isapplied in which N transform coefficients need to be decoded, thusincreasing decoding efficiency. That is, according to S730, (inverse)transform efficiency and decoding efficiency of the decoding apparatus300 may be increased through the inverse LFNST.

The following drawings are provided to describe specific examples of thepresent disclosure. Since the specific designations of devices or thedesignations of specific signals/messages/fields illustrated in thedrawings are provided for illustration, technical features of thepresent disclosure are not limited to specific designations used in thefollowing drawings.

FIG. 8 is a flowchart illustrating an operation of a video encodingapparatus according to an embodiment of the present disclosure.

Each operation illustrated in FIG. 8 may be performed by the encodingapparatus 200 illustrated in FIG. 2. Specifically, S810 may be performedby the predictor illustrated in FIG. 2, S820 may be performed by thesubtractor 231 illustrated in FIGS. 2, S830 and S840 may be performed bythe transformer 232 illustrated in FIG. 2, and S850 may be performed bythe quantizer 233 and the entropy encoder 240 illustrated in FIG. 2.Operations according to S810 to S850 are based on some of contentsdescribed in FIG. 4 to FIG. 6. Therefore, a description of specificdetails overlapping with those explained above with reference to FIG. 2and FIG. 4 to FIG. 6 will be omitted or will be made briefly.

The encoding apparatus 200 according to an embodiment may deriveprediction samples based on the intra prediction mode applied to thetarget block (S810).

The encoding apparatus 200 according to an embodiment may deriveresidual samples for the target block based on the prediction samples(S820).

The encoding apparatus 200 according to an embodiment may derivetransform coefficients for the target block based on a primary transformfor the residual samples (S830).

The primary transform may be performed through a plurality of transformkernels, and in this case, a transform kernel may be selected based onthe intra prediction mode.

The encoding apparatus 200 may perform a secondary transform or anon-separable transform, specifically LFNST, on transform coefficientsfor a target block.

The encoding apparatus 200 according to an embodiment may derivemodified transform coefficients for the target block based on the LFNSTfor the transform coefficient when the size of the target block is equalto or smaller than the size of the predetermined maximum transformapplied block. (S840).

The size of the maximum transform applied block may be set to the sizeof the transform block, for example, the maximum size of the transformblock. For example, if the size of the maximum transform block is 64×64,the size of the maximum transform applied block is set to 64×64 or 64,and if the size of the maximum transform block is 32×32, the size of themaximum transform applied block may be set to 32×32 or 32.

The encoding apparatus 200 may determine whether the non-separabletransform is performed through comparison of any one of the width orheight of the target block, for example, a large value with the size ofthe maximum transform applied block, that is, the width or height of themaximum transform applied block.

Alternatively, if the size of the target block is larger than the sizeof the predetermined maximum transform applied block, the lfnst indexindicating the predetermined transform kernel matrix used for thenon-separable transform may not be derived. That is, if the size of thetarget block is larger than the size of the predetermined maximumtransform applied block, the lfnst index may not be encoded. If thelfnst index is not encoded, the lfnst index is inferred to as 0 and theLFNST is not applied to the target block.

Meanwhile, the target block may be a coding block according to anexample, and may be a luma coding block and a chroma coding blockaccording to a color index. According to an example, if the size of theluma coding block is less than or equal to the size of the maximumtransform applied block and the color format is 4:2:0, the non-separabletransform may be performed on the chroma coding block when it is lessthan or equal to ½ the size of the maximum transform applied block. Thatis, the inverse LFNST may be applied to the chroma block having a widthand a height obtained by dividing the width and height of the luma blockby two. For example, since the inverse LFNST can be applied when thesize of the luma block is equal to or smaller than the 64×64 block, theLFNST can be applied when the size of the chroma block is equal to orsmaller than the 32×32 block when the color format is 4:2:0.

In one example, the LFNST may be performed based on a simplifiedtransform matrix or a transform kernel matrix, and the simplifiedtransform matrix may be a non-square matrix in which the number of rowsis less than the number of columns.

In one embodiment, S840 may include determining whether the conditionsfor applying the LFNST are satisfied, generating and encoding the LFNSTindex based on the determination, selecting a transform kernel matrixand applying the LFNST to residual samples based on the selectedtransform kernel matrix and/or the simplification factor when theconditions for applying LFNST is satisfied. In this case, the size ofthe simplification transform matrix may be determined based on thesimplification factor.

On the other hand, when the LFNST is not applied, only the MTS-basedprimary transform procedure may be applied in the transform procedure asdescribed above. That is, the encoding apparatus may determine whetherthe LFNST is applied to the current block as in the above-describedembodiment, and when the LFNST is not applied, the encoding apparatusmay derive transform coefficients from residual samples through theprimary transform.

This primary transform procedure may be referred to as a primarytransform procedure or an MTS transform procedure. Such an MTS-basedprimary transform procedure may also be omitted in some cases.

The encoding apparatus 200 according to an embodiment may derivequantized transform coefficients by performing quantization based on themodified transform coefficients for the target block, and may encodeinformation about the quantized transform coefficients and an LFNSTindex (S850). That is, the encoding apparatus may generate residualinformation including information on quantized transform coefficients.The residual information may include the above-described transformrelated information/syntax element. The encoding apparatus may encodeimage/video information including residual information and output theencoded image/video information in the form of a bitstream.

More specifically, the encoding apparatus 200 may generate informationabout the quantized transform coefficients and encode the informationabout the generated quantized transform coefficients.

In one example, information on the quantized transform coefficients mayinclude at least one of information on whether LFNST is applied,information on a simplification factor, information on a minimumtransform size to which LFNST is applied, and information on a maximumtransform size to which LFNST is applied.

Also, the encoding apparatus 200 may encode information on the size ofthe maximum transform applied block, for example, flag information suchas sps_max_luma_transform_size_64_flag, at the sequence parameter setlevel.

Referring to S840, it can be confirmed that transform coefficients forthe target block are derived based on the LFNST for the residualsamples. Regarding the size of a transform kernel matrix, the size of ageneral transform kernel matrix is N×N, while the size of a simplifiedtransform matrix is reduced to R×N, thus making it possible to reducememory occupancy by an R/N ratio when performing the RST compared towhen performing a general transform. Further, compared to the number ofmultiplication operations, N×N, when using the general transform kernelmatrix, it is possible to reduce the number of multiplication operationsby an R/N ratio (to R×N) when the simplified transform kernel matrix isused. In addition, since only R transform coefficients are derived whenthe RST is applied, the total number of transform coefficients for thetarget block may be reduced from N to R, compared to when the generaltransform is applied in which N transform coefficients are derived, thusreducing the amount of data transmitted by the encoding apparatus 200 tothe decoding apparatus 300. That is, according to S840, transformefficiency and coding efficiency of the encoding apparatus 200 may beincreased through the LFNST.

In the present disclosure, at least one of quantization/dequantizationand/or transform/inverse transform may be omitted. Whenquantization/dequantization is omitted, a quantized transformcoefficient may be referred to as a transform coefficient. Whentransform/inverse transform is omitted, the transform coefficient may bereferred to as a coefficient or a residual coefficient, or may still bereferred to as a transform coefficient for consistency of expression.

In addition, in the present disclosure, a quantized transformcoefficient and a transform coefficient may be referred to as atransform coefficient and a scaled transform coefficient, respectively.In this case, residual information may include information on atransform coefficient(s), and the information on the transformcoefficient(s) may be signaled through a residual coding syntax.Transform coefficients may be derived based on the residual information(or information on the transform coefficient(s)), and scaled transformcoefficients may be derived through inverse transform (scaling) of thetransform coefficients. Residual samples may be derived based on theinverse transform (transform) of the scaled transform coefficients.These details may also be applied/expressed in other parts of thepresent disclosure.

In the above-described embodiments, the methods are explained on thebasis of flowcharts by means of a series of steps or blocks, but thepresent disclosure is not limited to the order of steps, and a certainstep may be performed in order or step different from that describedabove, or concurrently with another step. Further, it may be understoodby a person having ordinary skill in the art that the steps shown in aflowchart are not exclusive, and that another step may be incorporatedor one or more steps of the flowchart may be removed without affectingthe scope of the present disclosure.

The above-described methods according to the present disclosure may beimplemented as a software form, and an encoding apparatus and/ordecoding apparatus according to the disclosure may be included in adevice for image processing, such as, a TV, a computer, a smartphone, aset-top box, a display device or the like.

When embodiments in the present disclosure are embodied by software, theabove-described methods may be embodied as modules (processes, functionsor the like) to perform the above-described functions. The modules maybe stored in a memory and may be executed by a processor. The memory maybe inside or outside the processor and may be connected to the processorin various well-known manners. The processor may include anapplication-specific integrated circuit (ASIC), other chipset, logiccircuit, and/or a data processing device. The memory may include aread-only memory (ROM), a random access memory (RAM), a flash memory, amemory card, a storage medium, and/or other storage device. That is,embodiments described in the present disclosure may be embodied andperformed on a processor, a microprocessor, a controller or a chip. Forexample, function units shown in each drawing may be embodied andperformed on a computer, a processor, a microprocessor, a controller ora chip.

Further, the decoding apparatus and the encoding apparatus to which thepresent disclosure is applied, may be included in a multimediabroadcasting transceiver, a mobile communication terminal, a home cinemavideo device, a digital cinema video device, a surveillance camera, avideo chat device, a real time communication device such as videocommunication, a mobile streaming device, a storage medium, a camcorder,a video on demand (VoD) service providing device, an over the top (OTT)video device, an Internet streaming service providing device, athree-dimensional (3D) video device, a video telephony video device, anda medical video device, and may be used to process a video signal or adata signal. For example, the over the top (OTT) video device mayinclude a game console, a Blu-ray player, an Internet access TV, a Hometheater system, a smartphone, a Tablet PC, a digital video recorder(DVR) and the like.

In addition, the processing method to which the present disclosure isapplied, may be produced in the form of a program executed by acomputer, and be stored in a computer-readable recording medium.Multimedia data having a data structure according to the presentdisclosure may also be stored in a computer-readable recording medium.The computer-readable recording medium includes all kinds of storagedevices and distributed storage devices in which computer-readable dataare stored. The computer-readable recording medium may include, forexample, a Blu-ray Disc (BD), a universal serial bus (USB), a ROM, aPROM, an EPROM, an EEPROM, a RAM, a CD-ROM, a magnetic tape, a floppydisk, and an optical data storage device. Further, the computer-readablerecording medium includes media embodied in the form of a carrier wave(for example, transmission over the Internet). In addition, a bitstreamgenerated by the encoding method may be stored in a computer-readablerecording medium or transmitted through a wired or wirelesscommunication network. Additionally, the embodiments of the presentdisclosure may be embodied as a computer program product by programcodes, and the program codes may be executed on a computer by theembodiments of the present disclosure. The program codes may be storedon a computer-readable carrier.

FIG. 9 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

Further, the contents streaming system to which the present disclosureis applied may largely include an encoding server, a streaming server, aweb server, a media storage, a user equipment, and a multimedia inputdevice.

The encoding server functions to compress to digital data the contentsinput from the multimedia input devices, such as the smart phone, thecamera, the camcoder and the like, to generate a bitstream, and totransmit it to the streaming server. As another example, in a case wherethe multimedia input device, such as, the smart phone, the camera, thecamcoder or the like, directly generates a bitstream, the encodingserver may be omitted. The bitstream may be generated by an encodingmethod or a bitstream generation method to which the present disclosureis applied. And the streaming server may store the bitstream temporarilyduring a process to transmit or receive the bitstream.

The streaming server transmits multimedia data to the user equipment onthe basis of a user's request through the web server, which functions asan instrument that informs a user of what service there is. When theuser requests a service which the user wants, the web server transfersthe request to the streaming server, and the streaming server transmitsmultimedia data to the user. In this regard, the contents streamingsystem may include a separate control server, and in this case, thecontrol server functions to control commands/responses betweenrespective equipments in the content streaming system.

The streaming server may receive contents from the media storage and/orthe encoding server. For example, in a case the contents are receivedfrom the encoding server, the contents may be received in real time. Inthis case, the streaming server may store the bitstream for apredetermined period of time to provide the streaming service smoothly.

For example, the user equipment may include a mobile phone, a smartphone, a laptop computer, a digital broadcasting terminal, a personaldigital assistant (PDA), a portable multimedia player (PMP), anavigation, a slate PC, a tablet PC, an ultrabook, a wearable device(e.g., a watch-type terminal (smart watch), a glass-type terminal (smartglass), a head mounted display (HMD)), a digital TV, a desktop computer,a digital signage or the like. Each of servers in the contents streamingsystem may be operated as a distributed server, and in this case, datareceived by each server may be processed in distributed manner.

Claims disclosed herein can be combined in a various way. For example,technical features of method claims of the present disclosure can becombined to be implemented or performed in an apparatus, and technicalfeatures of apparatus claims can be combined to be implemented orperformed in a method. Further, technical features of method claims andapparatus claims can be combined to be implemented or performed in anapparatus, and technical features of method claims and apparatus claimscan be combined to be implemented or performed in a method.

What is claimed is:
 1. An image decoding method performed by a decoding apparatus, the method comprising: receiving a bitstream including residual information; deriving transform coefficients for a target block based on the residual information; deriving modified transform coefficients based on an inverse non-separable transform for the transform coefficients; deriving residual samples for the target block based on an inverse primary transform for the modified transform coefficients; and generating a reconstructed picture based on the residual samples for the target block, wherein the inverse non-separable transform is performed based on the size of the target block being equal to or smaller than the size of a predetermined maximum transform applied block.
 2. The image decoding method of claim 1, wherein information on the size of the maximum transform applied block is further received.
 3. The image decoding method of claim 1, wherein whether the inverse non-separable transform is performed is derived by comparing the larger of the width or height of the target block with the width or height of the maximum transform applied block.
 4. The image decoding method of claim 1, wherein the size of the maximum transform applied block is 64×64.
 5. The image decoding method of claim 1, wherein when the size of the target block is larger than the size of the predetermined maximum transform applied block, an lfnst index indicating a predetermined transform kernel matrix used for the inverse non-separable transform is not derived.
 6. The image decoding method of claim 1, wherein the target block includes a luma coding block and a chroma coding block, wherein based on the size of the luma coding block being equal to or smaller than the size of the maximum transform applied block and a color format being 4:2:0, the inverse non-separable transform is performed when the chroma coding block is less than or equal to ½ of the size of the maximum transform applied block.
 7. An image encoding method performed by an image encoding apparatus, the method comprising: deriving prediction samples for a target block; deriving residual samples for the target block based on the prediction samples; deriving transform coefficients for the target block based on a primary transform for the residual samples; deriving modified transform coefficients from the transform coefficients based on a predetermined transform kernel matrix for a non-separate transform; and encoding the quantized residual information and an lfnst index indicating the transform kernel matrix, wherein the non-separable transform is performed based on the size of the target block being equal to or smaller than the size of a predetermined maximum transform applied block.
 8. The image encoding method of claim 7, wherein information on the size of the maximum transform applied block is further encoded.
 9. The image encoding method of claim 7, wherein whether the non-arable transform is performed is derived by comparing the larger of the width or height of the target block with the width or height of the maximum transform applied block.
 10. The image encoding method of claim 7, wherein the size of the maximum transform applied block is 64×64.
 11. The image encoding method of claim 7, wherein based on the size of the target block being larger than the size of the predetermined maximum transform applied block, the lfnst index is not encoded.
 12. The image encoding method of claim 7, wherein the target block includes a luma coding block and a chroma coding block, wherein based on the size of the luma coding block being equal to or smaller than the size of the maximum transform applied block and a color format being 4:2:0, the non-separable transform is performed when the chroma coding block is less than or equal to ½ of the size of the maximum transform applied block.
 13. A computer-readable digital storage medium that stores a bitstream generated by a method, the method comprising: deriving prediction samples for a target block; deriving residual samples for the target block based on the prediction samples; deriving transform coefficients for the target block based on a primary transform for the residual samples; deriving modified transform coefficients from the transform coefficients based on a predetermined transform kernel matrix for a non-separate transform; and encoding the quantized residual information and an lfnst index indicating the transform kernel matrix to generate the bitstream, wherein the non-separable transform is performed based on the size of the target block being equal to or smaller than the size of a predetermined maximum transform applied block. 